High-order exponential integrators for the Riesz space-fractional telegraph equation

In this paper, we study the numerical solution of a class of Riesz space fractional telegraph equation. In the spatial direction, the equations are discretized using the fractional central difference scheme, and an equivalent semi-linear form is obtained. Then, a fourth-order exponential Runge-Kutta method is chosen in the temporal direction. Moreover, an efficient method for calculating the matrix exponent and matrix phi-function is proposed by performing a series of matrix transformations on the coefficient matrix in the semi-linear form, improving the efficiency of the matrix functions calculation. Several numerical experiments show that the convergence order of the scheme is O(h(2) + tau(4)), where h is the space step and tau is the time step. The effectiveness of the scheme is also verified.

Automated summary

This paper studies the numerical solution of a class of Riesz space fractional telegraph equation. The equations are discretized using the fractional central difference scheme in the spatial direction and a fourth-order exponential Runge-Kutta method is chosen in the temporal direction. An efficient method for calculating the matrix exponent and matrix phi-function is proposed, improving the efficiency of the matrix functions calculation. Numerical experiments demonstrate the convergence order and effectiveness of the scheme.